Wonk City: More on Deflation and Interest Rates

My once and future dream is that the blogosphere would replace academic journals as the primary medium of intellectual exchange. We are far, far, far from that but this debate over deflation is getting sufficiently wonky that a boy can dream. If only there was some easy way to incorporate an equation editor into a blog writer, we would be off to the races.

What [Krugman, Rowe, Thoma and Harless] are objecting to in Kocherlakota’s speech is one of the most innocuous things he said. Here’s the simplest example I know. Suppose a cash-in-advance model with a representative consumer, period utility u(c), discount factor b, constant aggregate endowment y. c is consumption. The consumer needs cash to buy c each period. Suppose y is a fixed quantity of output received by a firm, which is sold for cash within the period, and then the cash is paid as a dividend to the consumer at the end of the period. Have the money stock grow at a constant rate m. The real interest rate is constant at 1/b -1. The nominal interest rate is (1+m)/b – 1, and the inflation rate is m. Constant m implies a constant nominal interest rate and a constant inflation rate. If m < 0, there is deflation, and the nominal interest rate is sufficiently low to support the deflation. I can think of the instrument the central bank sets as either the money growth rate or the nominal interest rate – that part is irrelevant. This type of result holds in virtually all monetary models, though of course sometimes the real rate may depend on the inflation rate. That’s not a big deal though. What’s the problem?

Let me say again. There is absolutely nothing inaccurate about what Williamson is saying. It falls simply and elegantly out of our monetary models.

The blogosphere is reacting with shock and despair because the conclusion doesn’t look anything like what they would expect to happen in the real world. In the real world if the Fed set a permanent low interest rate target all of our intuition, training and observations say that the result will be hyperinflation not deflation.

The question is: How can we reconcile the two?

As is often the case the key difference is hidden in a seemingly innocuous turn-of-phrase. Williamson writes

I can think of the instrument the central bank sets as either the money growth rate or the nominal interest rate – that part is irrelevant.

In some sense what Williamson is saying here is a mathematical necessity. For every nominal interest rate there exists some path of money which is consistent with it. I can choose one, or I can choose the other.

Where the confusion sets in is that a semi-plausible sounding nominal interest rate target can mathematically imply an obviously insane path for money. Yes, there is a one-to-one correspondence between the two in fact. Where the correspondence breaks down is in intuition.

For our particular example, we are considering a permanent nominal interest rate of .25% On the surface that seems like an, odd, perhaps dangerous, but doable goal. In reality its bat shit crazy and no one would ever believe that the Fed even had the ability to do it. Allow me to explain.

If the Fed is truly committed to a .25% nominal interest come-what-may then it is committed to expanding the money supply as rapidly as money demand requires. It doesn’t matter how many trillions upon trillions of reserves are required to meet that target, the Fed has committed to meeting it.

The key element you have to rap your mind around is that the Fed is doing this irrespective of the consequences. You have, for the purposes of this thought experiment, fixed the nominal interest rate for all time.

Now then what happens out in the real world.

Well, a permanent short term nominal rate of .25% means that long term rates must also be .25%. Is there some bend to the yield curve? Aren’t investors worried about inflation, deflation, etc? No, they are worried about nothing because the Fed is absolutely going to keep short term nominal rates at .25%. This is fixed and forever true.

If long term rates were any different then I could simply arbitrage the two and make a guaranteed profit. So all long rates are now .25%.

This means that Fannie / Freddie mortgage rates collapse to around .25%. Remember there is no prepayment risk in this world because interest rates will always and forevermore be .25%. In addition, there is virtually no risk to 30 year interest-only balloon mortgages, because rates will always be .25%. So that means I could borrow 300K for my home and my monthly payment to the bank would be $62.50. So we have essentially free mortgages.

Car loans collapse to .25% plus risk premium. Credit Card offers come through the mail that say 0% APR on all purchases, all balance transfers, all cash advances (plus 3% processing fee) FOREVER. Credit Cards can do this because the cost of funds is only .25% and they make 3% off the merchant fees. Add in the profits from late fees and there is no need to charge the on-time customer a dime, ever.

Similarly, corporate bond rates collapse. Mergers and Acquisitions fly into high gear as massive leveraged by-outs sweep Wall Street. There is nearly free money FOREVER. If you think you can get a return on equity of at least .25% in all periods then buying the company is a slam dunk.

All of this activity sends stock prices sky high, it sends home prices sky high, it sends commercial real estate sky high. The massive increase in paper wealth accompanied by free credit card purchases sends consumers on the shopping binge of a lifetime. The real economy goes white hot, and items are flying off of store shelves. Prices on everything rise: food, soap, paper towels, you name it, they can’t keep it in the store. There is free money – forever – and we are all rich.

In short, the result is massive inflation. This inflation would tend to push up nominal interest rates via the Fisher Effect. However, it can’t because the Fed is committed to .25% come-what-may.

That means that the Fed accelerates the expansion of the money supply so that even given huge inflation expectations the nominal interest rate stays low. This in turn feeds more inflation expectations which feeds more money creation and so on and so on.

Literally the continuous time models tell us that the inflation rate reaches infinity. That is,we shoot to a new, higher price level in zero time. That price level is one that is consistent with stock and home prices being discounted at .25% forever. The price level would have to be such that people as wealthy as they would be from those asset prices and with as easy access to credit as would come from 0% APR FOREVER, still would not want to purchase more output than the economy was capable of producing.

Needless to say these are extremely high prices since people can borrow so cheaply knowing that on paper they are so wealthy.

Like I said, inside the model this happens in zero time. That’s of course because inside the model everyone knows, that everyone knows, that everyone knows . . . that this is the end equilibrium and everyone faces zero costs to jumping straight to it.

So stores go ahead and figure out what the equilibrium price is and they just charge that. Same with homeowners, stock holders, etc. We see an instantaneous jump to a new equilibrium.

In the real world that is not possible. So, if the Fed tried such a policy it would get hyperinflation. It would get inflation that fed on itself in this same way but never actually reached an infinite rate. Eventually, however, we would hit the constraining price level.

What about the deflation?

Well with the nominal rate lower than the real rate, you want to engage in all possible investment today. By assumption in this model there are no adjustment costs so absent price constraints this would be possible. However, there is not an unlimited amount of investment goods and services to go around.

You want to build a thousand factories but there are not enough construction workers to do it. So construction prices go higher and higher to stop people from wanting to do it all today. However, this opens up an arbitrage opportunity.

As the owner of a construction firm, I can go to you and say, John, I know you want this factory built ASAP, but I’m a just completely booked. How about I do it for you next year for a little bit less? Are you willing to go for this?

Well if you don’t have the factory today you loose out on 1% of real return at a cost of only .25% in funds. So, if the factory is at least .75% cheaper next year its just as good of a deal for you to wait. So my firm offers you a cheaper deal next year and you agree to wait.

Next year, the same thing happens to another guy. He wants a factory now, but my firm is all booked up. Will he accept a .75% reduction in cost to wait? Yes, he will.

And the year-after-that, and the year-after-that, and the year-after-that.

So we have set ourselves up for permanent deflation in investment goods. It turns out the same thing has to be true in consumption as well. That’s because way back in the back of this model is a condition that essentially causes the average social discount rate to be equal to the real rate of interest.

That is, our society wide willingness to forgo consumption has to on average be the same as the return on investment. This means that as a society we are also willing to wait on the new TV or the new Ipad if we know its going to be cheaper later. In practice that would mean some people can’t wait and some people will be more than willing to wait. But, getting the average willingness to wait to match up with the realities of production will require .75% price drops each year. Again, permanent deflation.

So that’s how the model works its way into real life. A commitment to a permanent .25% nominal interest rate would produce permanent deflation but only after a raging period of hyperinflation.

Such a period would be so insane that no one would believe the Fed had the stones to see it through. That’s part of why the argument: a permanently low rate leads to deflation seems so insane to most economists. The process of getting to deflation would be violent and likely untenable.

I meant THEY accelerate the expansion of the money supply. They being the Fed. I broke down and did some cleaning. Hopefully its easier to read.

No I appreciate your comments even though I don’t always respond. My take is that the models aren’t actually the problem. Its understanding their limits when you translate back into reality.

So maybe a model has a term in which the limit goes to infinity. What does that actually mean in the real world. Some people will take it literally. Some people will ignore it. Some people will say it means the model is crap.

What it means, to me, is that the model has assumed away some factor this normally very very small but as the relevant quantities grow to infinity this factor grows as well and eventually becomes large enough to change your results.

That’s just one answer. For rationality for example, you have to hold in your mind the caveat that “as long as we can approximate with rationality” and be serious about what that means. If rationality fails then exactly which parts of your model don’t go through. That’s what you want to look at.

You don’t want to blindly accept rationality nor do you want to toss the whole model because it has a rationality assumption.

I often tell my students that in physics we assume that all of the mass of an object is concentrated at the center of gravity. This works fine until you run into the side of the object and find, “whoops, its corner actually does display inertia”

The center-of-gravity assumption doesn’t make the model crap but you do have to be aware of its limitations.

And when reality and the model differ, the physicist will modify his model. In fact, comparing the model to the real world and observing the differences gives us deeper insights into the real world, and, thus, better models.

My impression, though, is that The Economist, on the other hand, will ignore, explain away, or otherwise deny the reality. Thus, during the depression, the unemployed chose not to work. Keynes recognized the absurdity of this position, and modified the model to better approximate the reality.

This seemed to garner some respect for a while, but over the last 30 years he has been reviled, and all the lessons of the great depression have been systematically unlearned.

How can the construction firm owner commit to building the factory for a lower price next year? If they’re in an inflationary spiral, then the cost of materials and labor will be higher next year…which means that to maintain his firm’s real profit margin, the owner will need to charge you more next year, not less.

And why would he offer you this deal anyway? His construction firm is turning away customers…he’s not going to cut you any special deals.

However, from the firm owners point of view he has lots of orders for today. But no orders for next year. Yet, he plans to be in business next year. Why not lock up some future business by just lowering the price a bit.

Maybe he’s worried about the cost of materials. So he calls his materials guys, who is facing the exact same problem and offers the exact same deal.

Same thing with his workers, he can sign a contract garunteeing them work next year at a slightly low level.

Now for all this to work everyone has to UNDERSTAND that this is the world they live in. In reality not everyone will understand that. That’s part of why its not just a rapid bump up and then smooth deflation.

Its a violent relatively long (possibly several years or more) period of hyperinflation followed by the slow realization that deflation can be in your businesses best interest.

But why would the construction firm owner be worried about a lack of business next year? There was plenty of work this year, why wouldn’t there be plenty of work next year too?

Why would he lock himself into a commitment to charge less next year when there should be just as much reason to believe that he could charge even more next year???

For instance maybe one of his competitors will go out of business next year and he will have more pricing power.

I would think that, unless he has some specific reason to fear that next year there will be less work available for his firm, he should keep his options open.

Presumably the real profit margins in his business are set by how hard it is to get into that line of business. High barriers to entry will result in high profit margins. Low barriers to entry in low profit margins.

If his profit margins are already at the optimal level for the competition that he faces from other construction firms, why would he lower his prices further on contracts next year…UNLESS he has reason to believe that demand will slacken next year…but what would make him believe that?

Thanks for your interesting analysis on this – it’s helped me clarify my thinking on the question. I have come up with an analogy which I hope may be helpful for other readers: the truck-on-a-hill metaphor. Not a perfect analogy of course, but it helps bridge the gap between intuition and the theoretical model.

What you are describing as already happened: the “insane hyperinflation” happened in property prices (while the nominal rate went as low as 1% if I recall) and the US is currently in the “permanent deflation” stage. With the nominal rate at 0.25% for an indefinite period.